Wednesday, January 08, 2014

Folklore has it that VIX is a reasonable leading indicator of risk. Presumably that means if VIX is high, then there is a good chance that the future return of the SP500 will be negative. While I have found some evidence that this is true when VIX is particularly elevated, say above 30, I don't know if anyone has established a negative correlation between VIX and future returns. (Contemporaneous VIX and SP500 levels do have a very nice linear relationship with negative slope.)

Interestingly, the situation is much clearer if we examine the Variance Risk Premium (VRP), which is defined as the difference between a model-free implied volatility (of which VIX is the most famous example) and the historical volatility over a recent period. The relationship between VRP and future returns is examined in a paper by Chevallier and Sevi in the context of OVX, which is the CBOE Crude Oil Volatility Index. They have found that there is a statistically significant negative linear relationship between VRP and future 1-month crude oil futures (CL) returns. The historical volatility is computed over 5-minute returns of the most recent trading day. (Why 5 minutes? Apparently this is long enough to avoid the artifactual volatility induced by bid-ask bounce, and short enough to truly sample intraday volatility.) If you believe in the prescience of options traders, it should not surprise you that the regression coefficient is negative (i.e. a high VRP predicts a lower future return).

I have tested a simple trading strategy based on this linear relationship. Instead of using monthly returns, I use VRP to predict daily returns of CL. It is very similar to a mean-reverting Bollinger band strategy, except that here the "Bollinger bands" are constructed out of moving first and third quartiles of VRP with a 90-day lookback. Given that VRP is far from normally distributed, I thought it is more sensible to use quartiles rather than standard deviations to define the Bollinger bands. So we buy a front contract of CL and hold for just 1 day if VRP is below its moving first quartile, and short if VRP is above its moving third quartile. It gives a decent average annual return of 17%, but performance was poor in 2013.

Naturally, one can try this simple trading strategy on the E-mini SP500 future ES also. This time, VRP is VIX minus the historical volatility of ES. Contrary to folklore, I find that if we regress the future 1 day ES return against VRP, the regression coefficient is positive. This means that an increase of VIX relative to historical volatility actually predicts an increase in ES! (Does this mean investors are overpaying for put options on SPX for portfolio protection?) Indeed, the opposite trading rules from the above give positive returns: we should buy ES if VRP is above its moving third quartile, and short ES if VRP is below its moving first quartile. The annualized return is 6%, but performance in 2013 was also poor.

As the authors of the paper noted, whether or not VRP is a strong enough stand-alone predictor of returns, it is probably useful as an additional factor in a multi-factor model for CL and ES. If any reader know of other volatility index like VIX and OVX, please do share with us in the comments section!

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My online Backtesting Workshop will be offered on February 18-19. Please visit epchan.com/my-workshops for registration details. Furthermore, I will be teaching my Mean Reversion, Momentum, and Millisecond Frequency Trading workshops in London on March 17-21, and in Hong Kong on June 17-20.

What is a typical IP (intellectual property right) clause in a hedge fund contract? Is is standard that all models you develop may not be used when you move to a new firm? And how do you define a "model", is it exactly the same code or more loosely the concept? These seem to be tricky issues.

Hi Anon,Each contract is different of course.But most probably you can't take the software code from one fund to another. Whether you can take the trading idea or not is more murky and hard to define.Ernie

Hi ErnieHappy new year and thanks for the sharing.I am curious that given the R square being zero, how would you interpret the regression coefficient? I think whether it is positive or negative it doesnt have much indicative power?

I have found that whenever we are using linear regression for predicting future returns (as opposed to, say, finding the hedge ratio between two cointegrated ETFs), the R^2 is always close to 0.

This is not surprising because if the R^2 is significant, every trader in the world would be trading it already, erasing the predictability!

However, a R^2 close to zero does not mean that our trading strategy won't be profitable. That is the great irony of quantitative trading in contrast to most economic or commercial predictions. (I bet Walmart can predict next month's customer demand for a brand of toaster much better than I can predict tomorrow's SPX level!)

Following up on your discussion about R2. If you have a statistically significant coefficient and an R2 an epsilon above 0, you have slightly better odds than 50/50. Hence you should take that bet as often as possible, while of course managing your risk correctly.

Hi Anon,One can certainly sign a contract with one's employer with such favorable terms to you, though unless you are a well-known high-powered trader, I doubt many employers would opt for such a contract.

More typically, and by default, the employer owns all rights to your work there. Not only are you not entitled to royalties after termination, you are not permitted even to trade those models you developed during your employment.

First kind: you are not an employee, and often you have to risk your own capital to trade your model, though the firm will provide sky-high buying power (leverage). You typically own all IP in this situation.

Second kind: you are an employee and are paid a salary no matter your model is profitable or not. In this situation, it is no different from a hedge fund: the firm typically owns all IP.

Hi Anon,To start a fund, you would need to get a 3rd party administrator to assure people you won't take their money and run, and to prepare monthly statements. And you need to get a lawyer to write the Disclosure Document. Finally, you need to get accountant and auditor separately to prepare tax filings and annual audits. It is going to be expensive.

Typically, you would convince wealthy individuals to invest before you can convince institutional investors. Obviously you can do it in whichever order you think works for you.

I think it is much easier to start a managed account business than to start a fund.

So how does it usually work with managed accounts? I only need a simple company with an IB account to start hooking up managed accounts? Or I can even by an individual person (not a company of any form) that hook up managed accounts?

If you want to trade equity indices using a similar strategy you have an additional indicator, not available in crude space.

Namely you can use the same logic on the implied and historical correlation. Implied correlation you can back out by subtracting VIX from the mean ATM Black-Scholes implied volatility for each individual name in S&P 500. Similarly you can construct a CRP (correlation risk premium).

Since correlation and volatility in equities tend to move together CRP and VRP will be somewhat correlated. But my guess is that CRP might be more predictive than VRP for several reasons.

1) It's not directly observable like VIX, so less people probably trade on it. 2) Correlation tends to be more indicative of systematic risk than even volatility (correlations almost always go to 1 in crises). 3) Premiums for correlations indicate how many people are stock-picking vs indexing, which affects market dynamics.

Sorry, the previous list contains only indices available in Bloomberg. There are many more volatility indices calculated by CBOE using the variance swap replication method.http://www.cboe.com/micro/volatility/introduction.aspx.

Hello ErnieIn the chapter 6 of your new book,where you use TU as an example to illustrate the time series momentum strategy, I am confused with the concept "lagged roll return". How you define lagged roll return? Lagged Total Return minus lagged spot return?阮迅

I finally have enough confidence in my maths to work through your second book properly. I notice you make extensive use of the jplv7 econometrics toolbox. Is the textbook itself worth a purchase? I do have a ton of reading to do already, but if I don't buy books when I think of them, I just forget about them :)

I find out one of the famous proprietary trading firms in US has one of their 3 offices in Hong Kong, and the firm mainly uses stats arbitrage. What could be the possible reason that they choose Hong Kong for stats arbitrage? I cannot see there is any good stats arbitrage opportunity in HK market except they do something like index arbitrage. Besides, why would they hire traders to manually do stats arbitrage? Seem like the firm mainly uses their own money to trade so I guess their traders shouldn't be focus on entertaining clients.

Hi HK,Happy CNY!Just because a firm has office located in HK doesn't mean it is trading the HK markets. It may be trading Singaporean or Japanese stocks or futures.Algo trading shops still need "traders" because the software can break down from time to time.Ernie

I am thinking why the ETF of china market 2822, 2823 in Hong Kong Exchange don't move much after China market closes at 3pm, while the "GXC" SPDR S&P China ETF in USA market would have continuously movement in US trading hours. Could that because there are active ADRs of china stocks in US market while there is no ADR of china stocks in European market? There are a lot of H-share stocks in Hong Kong market that are main shares of China market, but seem like these H-share stocks would not affect 2822, 2823 pricing after 3pm while HK stock market closes at 4pm.

Thanks. The concept is very interesting that 2823 and 2822 suppose to follow the A50 future in SGX which trades 16 hours day, but the components inside 2822 and 2823 are A-shares real stocks/derivatives then they just don't move much after 3pm. I just check the A50 future SGX daily chart, and it looks like it keeps moving in 16 hours including that 3pm to 4pm period.

Let's say if I have 100K US dollars to buy a very popular huge trading volume stock for day trade, which case would have better chance to execute faster? Here are the two cases:1. 100K in one brokerage firm A2. 50K in brokerage firm A and 50K in brokerage firm B, both have buy command at the same time.

I checked and the interest cost to short etf/stock per trade within a day should be between 0.5% to 0.75% per trade for normal size retail account. So seem like this is too expensive to arbitrage for day trade especially ms speed range. So is that arbitrage day trade only makes sense for millions or more US dollars account to decrease the cost to reasonable level?

So, BTW, since no one else has asked, what were the returns for the two approaches in 2013 (or alternatively, what were the annual returns you came up with)? That would seem to be of great interest! Thank you!

Hello Ernie, This *might* be the most relevant blog post to ask this question, here goes:

From your experience as both an institutional trader and independent, do you think that being aware of prices/flows in the swaps markets (rates, volatility, correlation, etc) are of any use to a futures trader when trying to make more-informed decisions as to broad market sentiment for when the big boys are making significant moves? I can't help but wonder if there's a higher signal-to-noise ratio in the more liquid swaps, and that they might represent 'upstream' information. Then again, access to timely swaps market data might be tricky for a retail schlub such as I.

Hi Chad,Any data that is not commonly available can be useful, and swap data is no exception. I personally have not used this data because, as you said, it isn't readily available to retail traders or small funds like ourselves.Ernie